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Relevant bibliographies by topics / Polynomial subrings

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Academic literature on the topic 'Polynomial subrings'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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Journal articles on the topic "Polynomial subrings"

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NASR, MABROUK BEN, and NOÔMEN JARBOUI. "ON MAXIMAL NON-UNIVERSALLY CATENARIAN SUBRINGS." Journal of Algebra and Its Applications 07, no. 05 (2008): 553–56. http://dx.doi.org/10.1142/s021949880800293x.

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An integral domain R with field of fractions K is called a maximal non-1-catenarian subring of K if the polynomial ring in one variable, R[X] is not catenarian and for each proper intermediate ring T (that is each ring T such that R ⊂ T ⊆ K) T[X] is catenarian. The main purpose of this paper is to prove that the concept of maximal non-1-catenarian subrings and that of maximal non-universally catenarian subrings are equivalent.

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2

Shah, Tariq, and Ehsan Ullah. "Factorization properties of subrings in trigonometric polynomial rings." Publications de l'Institut Math?matique (Belgrade) 86, no. 100 (2009): 123–31. http://dx.doi.org/10.2298/pim0900123s.

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We explore the subrings in trigonometric polynomial rings and their factorization properties. Consider the ring S' of complex trigonometric polynomials over the field Q(i) (see [11]). We construct the subrings S'1 , S'0 of S' such that S'1 ?S'0 ?S'. Then S'1 is a Euclidean domain, whereas S'0 is a Noetherian HFD. We also characterize the irreducible elements of S'1, S'0 and discuss among these structures the condition: Let A ?B be a unitary (commutative) ring extension. For each x ? B there exist x' ?U(B) and x'' ? A such that x = x'x''. .

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ÖINERT, JOHAN, JOHAN RICHTER, and SERGEI D. SILVESTROV. "MAXIMAL COMMUTATIVE SUBRINGS AND SIMPLICITY OF ORE EXTENSIONS." Journal of Algebra and Its Applications 12, no. 04 (2013): 1250192. http://dx.doi.org/10.1142/s0219498812501927.

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The aim of this paper is to describe necessary and sufficient conditions for simplicity of Ore extension rings, with an emphasis on differential polynomial rings. We show that a differential polynomial ring, R[x; id R, δ], is simple if and only if its center is a field and R is δ-simple. When R is commutative we note that the centralizer of R in R[x; σ, δ] is a maximal commutative subring containing R and, in the case when σ = id R, we show that it intersects every nonzero ideal of R[x; id R, δ] nontrivially. Using this we show that if R is δ-simple and maximal commutative in R[x; id R, δ], th

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Ke¸pczyk, M., and E. R. Puczyłowski*. "RINGS WHICH ARE SUMS OF TWO SUBRINGS SATISFYING POLYNOMIAL IDENTITIES." Communications in Algebra 29, no. 5 (2001): 2059–65. http://dx.doi.org/10.1081/agb-100002168.

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Kȩpczyk, Marek. "Rings which are sums of PI subrings." Journal of Algebra and Its Applications 19, no. 08 (2019): 2050157. http://dx.doi.org/10.1142/s0219498820501571.

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We study rings [Formula: see text] which are sums of a subring [Formula: see text] and an additive subgroup [Formula: see text]. We prove that if [Formula: see text] is a prime radical ring and [Formula: see text] satisfies a polynomial identity, then [Formula: see text] is nilpotent modulo the prime radical of [Formula: see text]. Additionally, we show that if [Formula: see text] is a [Formula: see text] ring, then the prime radical of [Formula: see text] is nilpotent modulo the prime radical of [Formula: see text]. We also obtain a new condition equivalent to Koethe’s conjecture.

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6

ALHEVAZ, A., and A. MOUSSAVI. "ANNIHILATOR CONDITIONS IN MATRIX AND SKEW POLYNOMIAL RINGS." Journal of Algebra and Its Applications 11, no. 04 (2012): 1250079. http://dx.doi.org/10.1142/s021949881250079x.

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Let R be a ring with an endomorphism α and α-derivation δ. By [A. R. Nasr-Isfahani and A. Moussavi, Ore extensions of skew Armendariz rings, Comm. Algebra 36(2) (2008) 508–522], a ring R is called a skew Armendariz ring, if for polynomials f(x) = a0 + a1 x + ⋯ + anxn, g(x) = b0+b1x + ⋯ + bmxm in R[x; α, δ], f(x)g(x) = 0 implies a0bj = 0 for each 0 ≤ j ≤ m. In this paper, radicals of the skew polynomial ring R[x; α, δ], in terms of a skew Armendariz ring R, is determined. We prove that several properties transfer between R and R[x; α, δ], in case R is an α-compatible skew Armendariz ring. We al

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7

Kaygorodov, Ivan, Artem A. Lopatin, and Yury Popov. "Identities of sum of two PI-algebras in the case of positive characteristic." International Journal of Algebra and Computation 25, no. 08 (2015): 1265–73. http://dx.doi.org/10.1142/s021819671550040x.

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We consider the following question posted by Beidar and Mikhalev in 1995 for an associative ring [Formula: see text]: is it true that if the subrings [Formula: see text] and [Formula: see text] satisfy polynomial identities, then [Formula: see text] also satisfies a polynomial identity? Over a field of positive characteristic we establish new conditions on [Formula: see text] and [Formula: see text] that guarantee a positive answer to the question. We find upper and low bounds on the degrees of identities of [Formula: see text].

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8

Kȩpczyk, Marek. "Note on algebras which are sums of two PI subalgebras." Journal of Algebra and Its Applications 14, no. 10 (2015): 1550149. http://dx.doi.org/10.1142/s0219498815501492.

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We study an associative algebra A over an arbitrary field that is a sum of two subalgebras A1 and A2 (i.e. A = A1 + A2). Additionally we assume that Ai has an ideal of finite codimension in Ai which satisfies a polynomial identity fi = 0 for i = 1, 2. Suppose that all rings R = R1 + R2, which are sums of subrings R1 and R2, are PI rings when Ri satisfies the polynomial identity fi = 0 for i = 1, 2. We prove that A is a PI algebra.

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9

Chan, K., A. A. Young, and J. J. Zhang. "Discriminants and automorphism groups of Veronese subrings of skew polynomial rings." Mathematische Zeitschrift 288, no. 3-4 (2017): 1395–420. http://dx.doi.org/10.1007/s00209-017-1939-3.

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10

Beidar, K. I., and A. V. Mikhalev. "Generalized polynomial identities and rings which are sums of two subrings." Algebra and Logic 34, no. 1 (1995): 1–5. http://dx.doi.org/10.1007/bf00750549.

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Dissertations / Theses on the topic "Polynomial subrings"

1

Chapman, Scott T. (Scott Thomas). "Invertible Ideals and the Strong Two-Generator Property in Some Polynomial Subrings." Thesis, North Texas State University, 1987. https://digital.library.unt.edu/ark:/67531/metadc331673/.

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Let K be any field and Q be the rationals. Define K^1[X] = {f(X) e K[X]| the coefficient of X in f(X) is zero} and Q^1β[X] = {f(X) e Q[X]| the coefficent of β1(X) in the binomial expansion of f(X) is zero}, where {β1(X)}^∞ i=0 are the well-known binomial polynomials. In this work, I establish the following results: K^1[X] and Q^1β[X] are one-dimensional, Noetherian, non-Prüfer domains with the two-generator property on ideals. Using the unique factorization structure of the overrings K[X] and Q[X], the nonprincipal ideal structures of both rings are characterized, and from this characterizatio

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2

Snellman, Jan. "A graded subring of an inverse limit of polynomial rings." Doctoral thesis, Stockholm University, Department of Mathematics, 1998. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-543.

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<p>We study the power series ring R= K[[x<sub>1</sub>,x<sub>2</sub>,x<sub>3</sub>,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R.</p><p>Of particular interest are the homogeneous, finitely generated ideals in R', among them the <i>generic ideals</i>. The definition of S as an inverse limit yields a set of <i>truncation homomorphisms</i> from S to K[x<sub>1</sub>,...,x<su

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Books on the topic "Polynomial subrings"

1

Li, Hongnian. Projective modules over subrings of polynomial rings. 1992.

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Book chapters on the topic "Polynomial subrings"

1

Aschenbrenner, Matthias, Lou van den Dries, and Joris van der Hoeven. "Triangular Automorphisms." In Asymptotic Differential Algebra and Model Theory of Transseries. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175423.003.0013.

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This chapter focuses on triangular automorphisms, which can be analyzed by Lie techniques. Throughout the discussion K is a commutative ring containing ℚ as a subring. A formalism is introduced to analyze triangular automorphisms of such a polynomial algebra by means of their logarithms, the triangular derivations. After presenting some definitions and simple facts about filtered modules, filtered algebras, and graded algebras, the chapter considers triangular linear maps and the Lie algebra of an algebraic unitriangular group. It then describes derivations on the ring of column-finite matrices, along with iteration matrices and Riordan matrices. It also explains derivations on polynomial rings and concludes by applying triangular automorphisms to differential polynomials.

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